Bicep2has now concluded three years of observations at the South Pole. This data set contains over 14,000 hours of integration on our primary CMB field. Together with Bicep2’s increased mapping speed (over a factor of 10 relative to Bicep1), these observations constitute one of the deepest measurements of the degree-scale polarization of the CMB to date. This unprecedented sensitivity requires unprecedented control of instrumental polarization, ground pickup, sidelobes, magnetic response, and thermal pickup. We seek to demonstrate that each of these potential sources of systematics is well-below statistical uncertainty, and these efforts are ongoing.
The largest potential systematic forBicep2, mismatch of the pointing centers of detectors within a polarization pair, has been successfully mitigated using the deprojection analysis, as we will de- scribe in this section. A number of other analysis improvements used in the Bicep1 three-year analysis are readily applicable to the Bicep2 pipeline, including the likelihood estimation tech- nique, the improved bandpower window function calculation, and the deprojection of higher-order modes.
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1 0.5 0 0.5 1 1.5 2 2.5 3
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F-C 95% CI, 3 year Bayesian 95% CI, 3 year Data-derived value of ˆr
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r
Figure 5.7: Bayesian and frequentist constraints onrfrom theBicep1three-year data analysis. The frequentist confidence band is indicated by the white solid lines, while the 95% Bayesian credible interval is indicated with the dashed line. The observed value ofrˆ= 0.04is indicated by the dotted vertical line. Bayesian and Feldman-Cousins 95% confidence intervals, given the observed estimate, arer <0.7andr <0.63, respectively.
Efforts to publishBicep2spectra and new constraints on theB-mode polarization amplitude of the CMB are ongoing. While a large number of potential sources of systematics have been excluded through calibration measurements, data simulations, and data jackknives, new classes of potential systematics must be considered. Such possible candidates for potential systematics include, but are not limited to, contamination from cross-talk from the multiplexing architecture, near sidelobes, and magnetic pickup. Many of these sources have been demonstrated to be subdominant, but further analysis work is necessary.
In this section, we will presentBicep2sensitivity and map depth estimates, discuss the successful application of the deprojection algorithm to Bicep2, present some early analysis E and B-mode maps, and, lastly, discuss the path forward for theBicep2analysis.
5.7.1 Bicep2 sensitivity and map depth
Since deployment,Bicep2has achieved over an order-of-magnitude increase in mapping speed com- pared to Bicep1. This is owing primarily to three factors: Bicep2’s increased detector count, increased per-detector sensitivity (described in detail in Brevik et al. 2010), and increased observing efficiency. By reducing time spent on cryogenic operations and telescope turnarounds,Bicep2has been able to increase the fractional on-source time relative to Bicep1, as described in detail in Ogburn et al. 2010. Additionally, because of a string of highly successful engineering runs and a very efficient deployment,Bicep2suffered minimal downtime during the first few months of science data acquisition.
To compare the ultimate achievable sensitivities ofBicep1andBicep2, we calculate the average noise in the deepest regions of the Q and U maps. A single map depth statistic is not sufficient for estimating ultimate constraints on r, but rather serves as a point of comparison between the Bicep1andBicep2experiments. ForBicep1, the map depth is calculated for the deepest 200 deg2 of the field (based on integration time) co-added over three years of observations. Map-based noise estimates are drawn from noise simulations. We find the average Q/U map pixel noise in the deepest 200 deg2 to be 0.678 µK/deg2 and 0.50 µK/deg2 at 100 and 150 GHz, respectively. This is consistent with the 50% increase in data volume over theBicep1two-year analysis presented in Chiang et al. 2010, which reported a map depth in Q/U of 0.81 and 0.645 µK/deg2 at 100 and 150 GHz, respectively, for the same map area.
The Bicep2 three-year Q and U map depth is estimated in the same manner: A map area of 200 deg2 is selected based on the total integration time (exceeding 6.1⇥105 s). Rather than estimating noise from simulations, we estimate the noise directly from scan-direction Q and U jackknife maps (constructed from differencing left-going and right-going scans). The two map-based noise estimation methods (using scan direction versus noise simulations) will have strong agreement, so long as there is little correlated noise in the left and right going scans. For temperature maps,
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this is generally not the case, but for polarization maps, we find this to be true (particularly after ground subtraction).
From the jackknife maps, we find an averageQ/U map pixel rms of 0.089µK/deg2in the deepest 200 deg2 of our map. This is roughly consistent with noise estimates derived from the average per- detector sensitivity quoted in Ogburn et al. 2012 of 15.9 µKps, from which we calculate aQ/U map depth of 0.076µK/deg2.
5.7.2 Applying deprojection to Bicep2
As described in Section 3.1.4,Bicep2suffers from mismatch of detector centroids within a polarized pair (which we call differential pointing). Relative to other types of beam mismatch, differential pointing is by far the largest amplitude. As can be seen from Figure 5.2, the direction and mag- nitude of the differential pointing has a common-mode component shared between most detectors on the focal plane. For this reason,DK rotation provides a large cancelation of the contamination (because the beam displacement is rotated with respect to the field). Similarly, theDK jackknife, constructed by differencing observations separated by 180 degrees, is a powerful probe of common- mode differential pointing.
The deprojection algorithm, described in Section 4.4.2, has been successfully implemented to sup- press temperature-to-polarization leakage from differential pointing. The algorithm has undergone several improvements for the application to theBicep2data set. The largest of these improvements is to use spatial derivatives of the Planck 143 GHz temperature maps for the differential pointing templates. The Planck templates benefit from not only higher sensitivity detectors, but also higher resolution relative to the WMAP V-band maps used for the Bicep1 deprojection. Also, higher
nsidemaps were used to take full advantage of Planck’s higher resolution.
Figure 5.8 illustrates the application of the differential pointing deprojection algorithm toBicep2 two-yearE-mode maps. We examine the DK jackknife map, which, as previously mentioned, has the effect of amplifying the leakage of differential pointing relative to the nominal map. Before applying the deprojection algorithm, the leakage in the DK jackknife is booming – roughly the same amplitude as the E-mode signature itself. We again emphasize that the leakage in theDK jackknife map is enormously amplified relative to the leakage in the non-jackknife map because of the large leakage cancellation that results fromDK rotation.
After implementing the deprojection algorithm, we find that the signal in theDK jackknife map is enormously suppressed. We find that the post-deprojection DK jackknife map has comparable amplitude to signal-plus-noise simulations constructed assuming ideally matched pointing centers.
Given the additional suppression of the leakage fromDK rotation in non-jackknife maps, we find that differential pointing contributes negligible spurious polarization after deprojection.
Bicep2two-yearE Idealized two-year signal+noise sim
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Figure 5.8: Bicep2 two-year E-mode maps, filtered with an `-space spectral boxcar filter from 30 < ` < 400. Top row: The left-hand map shows the Bicep2 two-year E-mode map (with de- projection). The right-hand map shows a signal-plus-noise simulation, assuming ideally matched detector centroids. Middle row: The left-hand map shows the Bicep2 E-mode jackknife map, constructed by differencing observations separated by 180 deg inDK angle. This jackknife has the effect of amplifying common-mode differential pointing leakage. The right-hand map shows the same jackknife for the signal-plus-noise simulation. The signal component cancels exactly, since ideally matched pointing centroids have been assumed. Bottom row: The left-hand map shows the same DK jackknife map, but now after implementing the deprojection algorithm for differential pointing using the Planck 143 GHz temperature map. We find that the map amplitude is significantly re- duced when deprojection is implemented. The right-hand figure shows the idealized signal-plus-noise simulation with deprojection, which is largely unchanged after deprojection. Given the relative map amplitudes of the idealized signal-plus-noise simulated DK jackknife and the Bicep2 DK jack- knife after deprojection, we conclude that the cleaning algorithm is extremely effective at removing spurious polarization.
5.7.3 Bicep2 three-year map comparison
While the finalBicep2analysis is ongoing, it is illustrative to compareBicep1andBicep2three- year maps. TheBicep1maps used for this comparison are combined over 100 and 150 GHz, using the same methods and data selection as described in Section 5.5. TheBicep2 maps are co-added over three years, using the data selection summarized in Tables 4.1 and 4.2, extended to three years
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As in the case of Bicep1, the Bicep2 E- and B-mode maps have been constructed using a simple Fourier pseudo-C` estimator on the flat sky, and, as a result, both theBicep1 andBicep2 maps contain some non-zero E/B mixing. A comparison of Bicep1 and Bicep2 T, E, and B maps is plotted in Figure 5.9. Both maps have been masked with an identical integration time cut.
Owing to Bicep2’s higher detector count and higher observing efficiency, the map area observed with equal integration time is somewhat larger for Bicep2. The Bicep1 and Bicep2 maps are not identically filtered; theBicep1maps are smoothed to a 0.93 FWHM beam, while theBicep2 average beam width is 0.52 FWHM. This difference in beam-smoothing is clear in theT maps, but less obvious in theEandBmaps, since they have been further filtered with an`-space boxcar filter from 30<`<200. The polarization maps have also been apodized toward the map edges, where the map depth degrades.
Both T and E are measured with high significance. Additionally, the Bicep2 B maps are significantly deeper than the equivalentBicep1map. In the very near future, these Bicep2maps promise the most sensitive measurement of the degree-scale polarization of the CMB to date.
To illustrate the physics of theE-mode polarization, we can plot stacked hot and cold temperature anisotropies overlaid with polarization vectors extracted from Bicep2 three-year Q and U maps (Figure 5.10). We first locate local extrema in the map, which has been pre-smoothed to a beam width of = 0.5 degrees. We then stack and average both the temperature and polarization (Q and U) maps over these local maxima and minima, representing the polarization orientation and magnitude with headless vectors. We see a high degree of correlation between the magnitude and orientation of the polarization vectors relative to the hot and cold spots.
We can similarly co-add over hot and cold spots in theQandU maps. As before, local extrema are identified in the map, but now inQandU rather thanT. Different regions of the temperature and polarization maps are then co-located according to the locations of the extrema and then stacked and averaged. The result is plotted in Figure 5.11. As in Figure 5.10, the background image in each of the four tiles shows the stacked temperature anisotropy. Polarization vectors are overlaid in blue. The physical interpretation of this result is a bit more intuitive: We can immediately see that quadrupolar anisotropies in temperature give rise to linear polarization. The orientation of the polarization vector is directly tied to the orientation of the quadrupole. The temperature anisotropy in±Qis somewhat distorted by filtering along the scan direction, which is along the horizontal axis.
Bicep1T(100 + 150 GHz)/2 Bicep2T 150 GHz
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Figure 5.9: T, E and B-mode three-year maps for Bicep1 and Bicep2. The `-space filtering of the maps is not identical between the two sets of maps: TheBicep1maps have been smoothed to theBicep1 100 GHz equivalent beam width (0.93 ) for frequency combination, while theBicep2 average beam width is0.54degrees. The polarization maps have been further filtered with a boxcar filter from30<`<200.